Productive Failure II

This productive failure is from 2b on Exam 1. The answer I ended up putting frustrates me because I knew that it was obviosuly way too high of a number and made absolutely no sense, due to my knowledge that numbers in smaller bases appear higher than numbers in larger bases. I also was pretty sure that when adding together the bases that the last base was to the power of zero. For some reason however, I had in my notes that when we worked with decimals the ones place value right in front of the decimal was raised to the power of one instead of the power of zero. I must have confused it with the tenths place after the decimal being raised to the power of negative one instead of zero. I kept going back to this problem because I knew that my answer did not make sense and was incorrect but for some reason never attempted to see how it would come out if I changed the ones place value's base to the power of 0 and the tens to the power of 1. This is a very good productive failure to reflect on because it not only shows me that I need to make sure that my notes are completley correct but also that I needd to trust in myself and my knowledge and use that knowledge instead of relying on my notes. When I initially began this problem I was pretty positive that the base in the ones place started at the power of 0 and worked up but then saw my notes with the decimal and saw that it said with decimals we started with the ones place value's base raised to the power of 1. In conclusion, I think the decimal sort of scared me and made me think there was possibly a different rule. In the future, if I get an answer that I know does not make sense, I will have confidence and trust in my own knowledge and use the method that I initially thought true to see if it results in a more realistic answer.